A consumer has a utility function given by ln _U_ = 5 ln _x_1 + 3 ln _x_2 if the budget constraint is given by 10_x_1 + 14_x_2 = 124, find i) the optimal quantities of the two goods that the consumer should purchase in order to maximise utility, subject to the budget constraint. ii) the value of the consumer’s marginal utility of money at the optimum iii) the marginal rate of substitution (MRS) of _x_1 for _x_2 and determine its direction at the optimum

/in /by

A consumer has a utility function given by

ln _U_ = 5 ln _x_1 + 3 ln _x_2

if the budget constraint is given by

10_x_1 + 14_x_2 = 124, find

i)                  the optimal quantities of the
two goods that the consumer should purchase in order to maximise
utility, subject to the budget constraint.

ii)                the value of the consumer’s
marginal utility of money at the optimum

iii)              the marginal rate of substitution
(MRS) of _x_1 for _x_2 and determine its direction at the optimum

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